Accession Number:

AD0773658

Title:

The Method of Lie Series for Differential Equations and Its Extensions.

Descriptive Note:

Final technical rept.,

Corporate Author:

INNSBRUCK UNIV (AUSTRIA) INST OF MATHEMATICS

Personal Author(s):

• Wanner,G.
• Groebner,W.
• Fuchs,F.
• Hairer,E.
• Kirschner,O.

Report Date:

1973-09-01

Pagination or Media Count:

162.0

Abstract:

The work considers the initial value problem for an ordinary differential equation in a Banach space. The starting point of this research is Grobners notation, the so-called Lie series. An explicit computation of the two normal subgroups whose product is the orthogonal group and its transform is given. A general method for the numerical integration of ordinary differential equations is studied. This method includes in special cases the multi-step methods, Runge-Kutta methods multistage, Taylor series multi derivative and their extensions. Finally, Eulers Runge-Kutta methods of type IIIc are considered and their A-stability is proved. The implicit Eulers method is studied and is shown to be highly stable. An algorithm is implemented and numerical results are given. Author

Descriptors:

• *Differential equations
• *Numerical integration
• Boundary value problems
• Banach space
• Runge Kutta method
• Iterations
• Matrices(Mathematics)
• Austria

Subject Categories:

• Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE